1. Solve the following Non-Exact differential equations: [Hint : (M, - N2) = f(x)] [Hint :...

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1. Solve the following Non-Exact differential equations: [Hint : (M, - N2) = f(x)] [Hint : (N - My) = f(y)] (a) y(2x2 - ry + 1)dr + (x – y)dy = 0 (b) (3r2y +2ry)dr + (2a y3 - a²)dy = 0 %3D (c) y(y? – 2x2)da + x(2y? – a2)dy = 0 %3D IM+yN 3ry(y-r (d) (r2y? +ry+ 1)ydx + (a²y? – xy+ 1)xdy = 0 Hint : M-yN %3D [Hint : (My – N.) = f(x)] [Hint : I.F. = r"yk] (e) (ry - e")dr - a ydy 0 %3D (f) y(ry+ 2x2y³)dr +x(xy - a?y²)dy = 0 (g) (xy sin ry + cos ry)ydx + (ry sin ry – cos ry)rdy = 0 Hint : I.F. = - Ny (h) (2ryte" + 2ry³ + y)dr + (x²y*e – a?y? – 3x)dy = 0 [Hint : (N, - M,) = f(y)] 1. Solve the following Non-Exact differential equations: [Hint : (M, - N2) = f(x)] [Hint : (N - My) = f(y)] (a) y(2x2 - ry + 1)dr + (x – y)dy = 0 (b) (3r2y +2ry)dr + (2a y3 - a²)dy = 0 %3D (c) y(y? – 2x2)da + x(2y? – a2)dy = 0 %3D IM+yN 3ry(y-r (d) (r2y? +ry+ 1)ydx + (a²y? – xy+ 1)xdy = 0 Hint : M-yN %3D [Hint : (My – N.) = f(x)] [Hint : I.F. = r"yk] (e) (ry - e")dr - a ydy 0 %3D (f) y(ry+ 2x2y³)dr +x(xy - a?y²)dy = 0 (g) (xy sin ry + cos ry)ydx + (ry sin ry – cos ry)rdy = 0 Hint : I.F. = - Ny (h) (2ryte" + 2ry³ + y)dr + (x²y*e – a?y? – 3x)dy = 0 [Hint : (N, - M,) = f(y)]